Counterfactual Transition Graphs: Evaluating Cross-Class Transition Quality

Counterfactual (CF) explanations for time-series classifiers are usually evaluated one example at a time: what minimal edit flips this single window's prediction? We argue that the more informative question for diagnostic interpretability is structural: how does the classifier connect its own classes to each other? We propose a counterfactual transition graph (CGT) in which each node is a class and each edge weight is the CF reliability of the transition from one prototype to another under a proximity aware retrieval sweep. On a six-class hand-movement task, we induce a CGT that reveals a non-trivial topology, which is not predicted by the binary confusion matrix: it shows that counterfactual reachability does not align with classifier accuracy and even runs counter to it (Spearman ρ=-0.37 over the 15 pairs), i.e. the boundaries the classifier separates most confidently are among those an in-distribution edit can least often cross. Our framework is method agnostic, i.e. any CF-explainers can be used. Presently, we use it to juxtapose replacement-based CFs with gradient-based CFs; gradient-based methods reach almost any class by stepping off the data manifold, while replacement-based methods stay on it and fail on precisely the rigid boundaries.